國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Modular formsfundamental tools of ma...

Alfes-Neumann, Claudia.

Modular formsfundamental tools of mathematics /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Modular formsby Claudia Alfes-Neumann.
其他題名:	fundamental tools of mathematics /
作者:	Alfes-Neumann, Claudia.
出版者:	Wiesbaden :Springer Fachmedien Wiesbaden :2021.
面頁冊數:	vii, 41 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Forms, Modular.
電子資源:	https://doi.org/10.1007/978-3-658-34529-7
ISBN:	9783658345297$q(electronic bk.)

Modular formsfundamental tools of mathematics /
Alfes-Neumann, Claudia.

Modular formsfundamental tools of mathematics /[electronic resource] :by Claudia Alfes-Neumann. - Wiesbaden :Springer Fachmedien Wiesbaden :2021. - vii, 41 p. :ill., digital ;24 cm. - essentials. - essentials..

Fundamentals of complex analysis -- Modular forms -- Construction of modular forms and examples -- Hecke theory as well as L-functions of modular forms -- The partition function and modular forms of semi-integer weight -- Real-analytic modular forms.

In this essential, Claudia Alfes-Neumann discusses applications of the theory of modular forms and their importance as fundamental tools in mathematics. These functions - initially defined purely analytically - appear in many areas of mathematics: very prominently in number theory, but also in geometry, combinatorics, representation theory, and physics. After explaining necessary basics from complex analysis, the author defines modular forms and shows some applications in number theory. Furthermore, she takes up two important aspects of the theory surrounding modular forms: Hecke operators and L-functions of modular forms. The essentials concludes with an outlook on real-analytic generalizations of modular forms, which play an important role in current research. This Springer essential is a translation of the original German 1st edition essentials, Modulformen by Claudia Alfes-Neumann, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com) A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors. Contents Fundamentals of complex analysis Modular forms Construction of modular forms and examples Hecke theory and L-functions of modular forms The partition function and modular forms of half-integer weight Real-analytic modular forms The target groups Students of mathematics Non-specialist mathematicians and scientists The Author Prof. Dr. Claudia Alfes-Neumann is Professor of Mathematics at Bielefeld University.

ISBN: 9783658345297$q(electronic bk.)

Standard No.: 10.1007/978-3-658-34529-7doiSubjects--Topical Terms:

272963
Forms, Modular.

LC Class. No.: QA243 / .A54 2021

Dewey Class. No.: 512.73

Modular formsfundamental tools of mathematics /
LDR:03127nmm a2200349 a 4500 001 610733
003 DE-He213
005 20211011100526.0
006 m d
007 cr nn 008maaau
008 220330s2021 gw s 0 eng d
020 $a 9783658345297$q(electronic bk.)
020 $a 9783658345280$q(paper)
024 7 $a 10.1007/978-3-658-34529-7 $2 doi
035 $a 978-3-658-34529-7
040 $a GP $c GP
041 1 $a eng $h ger
050 4 $a QA243 $b .A54 2021
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.73 $2 23
090 $a QA243 $b .A386 2021
100 1 $a Alfes-Neumann, Claudia. $3 908915
240 1 0 $a Modulformen. $l English
245 1 0 $a Modular forms $h [electronic resource] : $b fundamental tools of mathematics / $c by Claudia Alfes-Neumann.
260 $a Wiesbaden : $b Springer Fachmedien Wiesbaden : $b Imprint: Springer, $c 2021.
300 $a vii, 41 p. : $b ill., digital ; $c 24 cm.
490 1 $a essentials
505 0 $a Fundamentals of complex analysis -- Modular forms -- Construction of modular forms and examples -- Hecke theory as well as L-functions of modular forms -- The partition function and modular forms of semi-integer weight -- Real-analytic modular forms.
520 $a In this essential, Claudia Alfes-Neumann discusses applications of the theory of modular forms and their importance as fundamental tools in mathematics. These functions - initially defined purely analytically - appear in many areas of mathematics: very prominently in number theory, but also in geometry, combinatorics, representation theory, and physics. After explaining necessary basics from complex analysis, the author defines modular forms and shows some applications in number theory. Furthermore, she takes up two important aspects of the theory surrounding modular forms: Hecke operators and L-functions of modular forms. The essentials concludes with an outlook on real-analytic generalizations of modular forms, which play an important role in current research. This Springer essential is a translation of the original German 1st edition essentials, Modulformen by Claudia Alfes-Neumann, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com) A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors. Contents Fundamentals of complex analysis Modular forms Construction of modular forms and examples Hecke theory and L-functions of modular forms The partition function and modular forms of half-integer weight Real-analytic modular forms The target groups Students of mathematics Non-specialist mathematicians and scientists The Author Prof. Dr. Claudia Alfes-Neumann is Professor of Mathematics at Bielefeld University.
650 0 $a Forms, Modular. $3 272963
650 1 4 $a Number Theory. $3 274059
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a essentials. $3 794391
856 4 0 $u https://doi.org/10.1007/978-3-658-34529-7
950 $a Mathematics and Statistics (SpringerNature-11649)